Reflecting Throughout the Day Take a moment and reflect on this morning and what you learned about bringing change to a district.

Implications of the Task Advocate and Systematize Collaborate and Implement Leadership of Self Know and Model Leadership of Self Know and Model Leadership of Others Leadership in the Extended Community

The primary purpose of Principles to Actions is to fill the gap between the adoption of rigorous standards and the enactment of practices, policies, programs, and actions required for successful implementation of those standards. Principles to Actions: Ensuring Mathematical Success for All

Frayer Model What is FLUENCY?

K-8 Fluencies

HS Fluencies

Build Procedural Fluency from Conceptual Understanding Procedural Fluency should: Build on a foundation of conceptual understanding; Result in generalized methods for solving problems; and Enable students to flexibly choose among methods to solve contextual and mathematical problems. Students must be able to do much more than carry out mathematical procedures. They must know which procedure is appropriate and most productive in a given situation, what a procedure accomplishes, and what kind of results to expect. Mechanical execution of procedures without understanding their mathematical basis often leads to bizarre results. Martin, 2009, p. 165

Warm-up Problem A candy jar contains 5 Jolly Ranchers (squares) and 13 Jawbreakers (circles). Suppose you had a new candy jar with the same ratio of Jolly Ranchers to Jawbreakers, but it contained 100 Jolly Ranchers. How many Jawbreakers would you have? Explain how you know. Please try to do this problem in as many ways as you can, both correct and incorrect. If done, share your work with a neighbor or look at the solutions on the back of the handout.

Principles to Actions Take a look at the table on the bottom of page 47 Looking at the transcript… – What does Mr. Donnelly say/do to build procedural fluency from conceptual understanding? – What do the students do to build procedural fluency from conceptual understanding? Discuss what you saw with a colleague. What suggestions do you have to move the lesson forward to facilitate building procedural fluency from conceptual understanding?

Procedural Fluency What might we expect the students in Mr. Donnelly’s class to be able to do when presented with a missing value problem, after they have had the opportunity to develop a set of strategies through solving a variety of contextual problems like the Candy Jar Task?

Procedural Fluency

Unit Rate Scaling Up Scale Factor

Next Steps with Principles to Actions— Leadership of Self & Others How could you use this activity with school/district teams?

Continued Study… 3 rd Fellows Meeting: Support productive struggle in learning mathematics 4 th Fellows Meeting: Elicit and use evidence of student thinking

Break

Making Number Talks Matter Ruth Parker “I’ve come to believe that my job is not to teach my students to see what I see. My job is to teach them to see.”

Number Talks Have any of you tried Number Talks in your classroom?

Starting Number Talks

What do DOT CARDS communicate about the culture of the classroom? What do DOT CARDS have to do with math?

“The power of Number Talks to transform peoples views of mathematics cannot be overstated, but there are other important goals that also can be achieved. Number Sense is the most important foundation that students can have and the basis for all higher-level mathematics. When students fail algebra, it is not because algebra is a really hard subject; it is because they do not have a foundation of number sense. As well as teaching students the math facts that they need to know, Number Talks teach students to understand the numerical relationships that are so critical to understanding mathematics.” p. viii Jo Boaler Making Number Talks Matter

Why start all students with DOT CARDS? All students only need to describe what they see allowing all of us to see how differently we can see things. Arithmetic problems tend to be emotionally loaded for many students and Number Talks are used to build a safe culture to explore thinking in a classroom.

Number Talk Practice Groups of 4 Each person will have a dot pattern to practice in their group What did you learn while practicing the number talks today?

Guiding Principles Mathematical ideas worth listening to; developing and expressing ideas Questioning to seek understanding Explaining conceptually rather than procedurally Valuing mistakes Efficiency of strategies Safe environment Social and Mathematical agency Time Confusion and Struggle Diversity

Planning a Number Talk

Next Steps with Number Talks — Leadership of Self & Others What can you commit to between now and our next meeting?

Summary - Leadership of self, others and the extended community Leadership Piece –Principles to Actions: Build Procedural Fluency from Conceptual Understanding Number Talk

Homework - Leadership of self, others and the extended community Try Number Talks in your classroom Meet with Admin and complete Action Plan Part B (Part B will be completed following each Fellows meeting) – Number Talks practice with staff members – Principles to Action Practices Principles to Action…Read Pgs. 48 to 52 (Support Productive Struggle in Learning Mathematics) by our next meeting

AESD Participant Survey Scan this QR code with your tablet or smartphone. (Note: You may need to download an app to allow scanning to work.)